Price collusion or competition in US higher education

Abstract

How geographical neighboring competitors influence the strategic price behaviors of universities is still unclear because previous studies assume spatial independence between universities. Using data from the National Center for Education Statistics college navigator dataset, this study shows that the price of one university is spatially autocorrelated to its neighboring competitors and such neighborhood structure induces cooperation Nash equilibrium in a spatial price game. In the spatial price game of universities the possibility of the cooperation solution is about 76%, while that of the defeat solution is about 24%. This study demonstrates that the relation between price difference and geographical distance of universities is an inverse U-shaped curve rather than a line.

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Studies in Higher Education
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Price collusion or competition in US higher
education
Jiafeng Gu
To cite this article: Jiafeng Gu (2015) Price collusion or competition in US higher education,
Studies in Higher Education, 40:2, 253-277, DOI: 10.1080/03075079.2013.823929
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Price collusion or competition in US higher education
Jiafeng Gu*
Institute of Social Survey Study, Peking University, Beijing, 100871, PR China
How geographical neighboring competitors influence the strategic price behaviors
of universities is still unclear because previous studies assume spatial independence
between universities. Using data from the National Center for Education Statistics
college navigator dataset, this study shows that the price of one university is
spatially autocorrelated to its neighboring competitors and such neighborhood
structure induces cooperation Nash equilibrium in a spatial price game. In the
spatial price game of universities the possibility of the cooperation solution is
about 76%, while that of the defeat solution is about 24%. This study
demonstrates that the relation between price difference and geographical distance
of universities is an inverse U-shaped curve rather than a line.
Keywords: price competition; strategic interaction; spatial game; reputation;
neighborhood size
1. Introduction
Since the US Justice Department’s Antitrust Division accused MIT and the Ivy League
schools of fixing prices in 1991, the vitriolic controversy over price collusion in higher
education field has not subsided (Kim 2010; Bamberger and Carlton 1999; Carlson and
Shepherd 1992; Salop and White 1991). The increasing tuition fees of US higher edu-
cation makes higher education institutes nervous, and the pricing mechanism of higher
education is increasingly being questioned (Ehrenberg 2000). Since the advent of a
regionally and nationally integrated market in which universities compete for both
resources and students (Hoxby 1997), higher education institutes vigorously compete
among themselves to attract the best students to their programs (Allen and Shen
1999) and the price competition among them has become very fierce and complex. It
seems that the price-setting behavior of higher education institutes has become a critical
topic of competitive justice.
The field of antitrust in higher education is not well established because of a theoretical
void (Wiley 1988). Some critical questions are still uninvestigated. With the prevalence of
price competition in higher education, has the line between collaboration and collusion
among higher education institutes been blurred? How does the competitive structure
affect the price-setting behavior and the ultimate performance of higher education?
There are some studies which implicitly acknowledge the possibility of pricing collusion
in higher education, including demand of college education (Clotfelter 1996) and federal
grants (Li 1999). Recently, spatial dynamics have been detected in the pricing of higher
education, and the price competition of higher education has become a space-dependent
© 2013 Society for Research into Higher Education
*Email: isssgujf@pku.edu.cn
Studies in Higher Education, 2015
Vol. 40, No. 2, 253–277, http://dx.doi.org/10.1080/03075079.2013.823929

game (McMillen, Singell and Waddell 2007). However, scholarly analysis of price collu-
sion in higher education is still in its infancy and an integrated analysis of antitrust policy
with the spatial pricing game in higher education is urgently needed.
2. Literature review and theoretical framework
As Adam Smith (1776) said, “business people too seldom gather, even for merriment
and diversion, without their talk soon turning to some contrivance or conspiracy against
the public”(Smith 1776, 137). When issues about the price of higher education were
discussed at Ivy Overlap Group meetings, it was suspected that some contrivance or
conspiracy was formulated against the public (Bamberger and Carlton 1999; Salop
and White 1991). When the US opened the Antitrust Investigation into Universities,
it sparked fierce debate. Obviously, the antitrust doctrine in the field of higher education
needs a more stable theoretical foundation. Recent game theory research, most promi-
nently by Robert Axelrod (1997), offers the hope of filling this theoretical void. McMil-
len, Singell and Waddell (2007) proved that there were price-setting practices among
universities, which responded to the geographic and qualitative proximity of competi-
tors; this implied that universities interacted preferentially with other universities in
their vicinity in the pricing process. In such spatial games, universities have at their dis-
posal certain pricing strategies; their payoffs depend on the pricing strategies chosen
both by them and by their opponents. When no university has an incentive to
deviate from his or her chosen price strategy after considering an opponent’s choice,
this is the Nash equilibrium. This raises an important question: if cooperation is a pre-
ferred Nash equilibrium in the spatial price game of higher education, what is the impli-
cation for the antitrust policy? This suggests an agenda for spatial game theory research
and its application to the antitrust doctrine, because such research has embodied a
different theory of reciprocity with spatial interactions among neighboring universities.
Conventional pricing wisdom of higher education holds that the price of higher edu-
cation mirrors different factors including location, quality of professors, courses, fellow
students, and social life. Leslie and Brinkman (1987) investigated the price response in
higher education. Their theory is called “student demand theory”,andwasfirst put
forward by Jackson and Weathersby (1975) and followed later by Savoca (1990),
Abraham and Clark (2006)andNeill(2009). The pricing behavior of universities has
also been investigated from the cost view (Grodsky and Jones 2007;Barry1997;
St. John 1990). Recently, the strategic interactions among universities have been analyzed,
and a spatial effect emerges in the pricing behavior of universities (Ordine and Rose 2008).
In these studies, although higher education is clearly outside the range of what normally is
viewed as commerce, price collusion is not a significant issue in the pricing process.
It is a major challenge to distinguish between legitimate competition and anti-com-
petitive conduct when spatial interaction is incorporated into antitrust analysis, and it is
increasingly recognized that spatial effects are important in the price of universities in a
competitive environment (Hoxby 1997). We can learn much about how strategic pro-
cesses in higher education work by taking context more seriously. This is an obser-
vation similar in spirit to Granovetter’s(1985) observation that “economic action is
embedded in structures of social relations.”The concept of embeddedness is treated
as synonymous with the notion that organizations are part of a larger institutional struc-
ture. However, the price-setting behavior of higher education institutes is embedded not
only in the social structure but also in spatial structure. The literature foresees different
possible behaviors of organizations sharing a similar resource space.
254 J. Gu

Multipoint contact markets theory (Gimeno and Woo 1999; Baum and Haveman
1997) and spatial multipoint competition theory (Haveman and Nonnemaker 2000)
argue that similarity may spur either competition or cooperation depending on the per-
ceptions of the actors, and how they conceive similar firms in the local competition
space. These studies focus on the structure of the industry and the position of the organ-
ization in order to understand when organizations cooperate (Jayachandran, Gimeno
and Varadarajan 1999). The multimarket contact hypothesis holds that more contacts
between firms competing in the same markets may induce more collusion (Spagnolo
1999). Because higher education institutes are organizations offering relatively homo-
geneous goods in several geographic markets, the application of the multimarket
contact hypothesis to higher education is straightforward. However, the hypothesis
that multimarket linkages between higher education institutes could lead to a stronger
collusion should be tested systematically. Higher education institutes are multiproduct
organizations: competition in research is more reputation related, whereas competition
for undergraduate education displays stronger spatial effects and is obviously related to
the underlying structure of each local market. Moreover, the higher education system is
composed of layers with different activity and spatial structure. However, we know
little about how multimarket presence influences the pricing competition of higher edu-
cation institutes.
In particular, the main question of interest which is crucial to antitrust policy in
higher education is how the territorially structured interaction at the local level and
reputation competition at the national level can promote cooperation or defeat in a
spatial pricing game of universities. More specifically, we aim to seek answers to the
following questions: what effects does reputation have on cooperation or defeat in a
spatial price game of higher education? What effects does reputation have on the
spatial price game of higher education? In other words, does spatial interaction and
reputation mechanism induce cooperation among neighboring universities? In the lit-
erature, such dynamic result of interdependence is commonly termed Nash equilibrium
in the spatial game frame. Nash equilibrium is said to occur when no player has an
incentive to deviate from his or her chosen strategy after considering an opponent’s
choice. Recent studies that have incorporated spatial dependence in the paradoxical
prisoner’s dilemma (PD) are, among others, the spatial distribution of individuals on
the outcome of competition in Durrett and Levin (1998), the evolution of cooperation
within the strategy space of all stochastic strategies in Brauchli, Killingback and
Doebeli (1999), the spatial competition in China’s higher education system (Jiafeng
2012a,2012c), the spatial interaction among China’s counties (Jiafeng 2012b) and
altruism in Fletcher and Zwick (2007). There was clear indication that this pricing be-
havior of universities was shaped by evolution of a spatial game in which the price one
university chooses depended on its neighboring universities’prices.
The present paper contributes to the existing literature by examining the spatial
pricing behavior of universities in a spatial evolutionary game frame (Ohtsuki et al.
2006; Szabó et al. 2000). Contrary to Robert Axelrod’s(1997) PD game, we use
100 top universities in USA and detect the spatial interactions among neighboring uni-
versities to investigate empirically the cooperation equilibrium nature of the spatial
game. To test the relationship between spatial structure and pricing strategies of univer-
sities, we use the spatial econometrics method. In traditional spatial evolutionary game
theory, the strategic interaction relationship between players is not tested, due to a silent
assumption that it is significant. In this paper, we will test the strategic interaction
assumption by spatial autocorrelation testing. Then we will investigate the effect of
Studies in Higher Education 255

spatial structure on the Nash equilibrium by incorporating neighborhood size into
spatial PD. Finally, we will investigate price determination dynamics by spatial
regression models. The evolution of spatial pricing games is of importance to the anti-
trust policy of higher education because the previous literature suggests not only that
the geographic location of universities plays an important role in the pricing process,
but also that the mechanism or mechanisms by which this price equilibrium occurs
may be identifiable.
3. Method
The analysis frame of this study is empirical spatial PD, in which Killingback, Doebeli,
and Knowlton (1999) introduced spatial structure, following the general approach of
spatial evolutionary game theory (Killingback and Doebeli 1996; Nowak and May
1992). The individual universities are placed in the cells of a lattice. Each individual
makes a decision about its price, and interacts with the individuals within its neighbor-
hood. The individual will get payoffs as prescribed by the rules of the game, when
playing against each of the neighbors within its interaction neighborhood. Its fitness
is then the sum of the payoffs it gets from playing against all its neighbors.
1
3.1 Data, sample, and variables
We select top 100 universities in USA from the US News ranking system. After iden-
tifying the top 100 universities in USA, we collect data of those universities from the
college navigator dataset of National Center for Education Statistics. We use the tuition
and fees, room and board and total expenses in 2006–2007, 2007–2008, 2008–2009
and 2009–2010 school years to test spatial interaction assumption. The descriptive stat-
istics of those variables are given in Table 1.
To test the spatial dynamics in pricing process of higher education, we also collect
characters of universities including undergraduate enrollment, type of university, per-
centage of full-time, first-time students who graduated in four years, percentage of stu-
dents receiving any financial aid, student-to-faculty ratio and total undergraduate
admissions in the 2008–2009 school year. We also collect the longitude and latitude
data of every university to implement spatial analysis.
The status competition theory claims that organizational reputation is important to
strategy researchers (Podolny 1993). Organizations with better reputations or higher
status tend to participate in more attractive upstream and downstream interactions
(Podolny 2008) and reputation is a valuable asset (Diamond 1991). At the same
time, the processes that generate reputations and status orderings can lead to the
Table 1. Descriptive statistics of the prices of universities (N= 100).
Tuition and fees Room and board Total expenses
Mean SD Mean SD Mean SD
2006–2007 26297 (7217.39) 8918.41 (1767.17) 38316.96 (8353.55)
2007–2008 27855.26 (7581.4) 9345.9 (1784.69) 40367.24 (8705.98)
2008–2009 29434.12 (7865.6) 9790.1 (1853.41) 42563.61 (9039.19)
2009–2010 30910.53 (7956.01) 10226.3 (1880.66) 44579.49 (9183.4)
256 J. Gu

heterogeneity of organizations (Podolny and Phillips 1996; Podolny and Page 1998).
We use the ranking as a reputational variable.
2
Each university has a ranking
number from 1 to 100. The smaller this ranking number is, the higher the university
ranks. The ranking number comes from the US News ranking system.
There is also a subsample in this study. To detect the spatial price behavior of uni-
versities, we use Harvard University as a benchmark and compute the difference of
tuition and fees in the 2008–2009 school year and the arc distance (1000 miles)
between Harvard University and other universities, respectively.
3
We exclude
Harvard University in this subsample and the number of units in this subsample is
99. The descriptive statistics of those variables are illustrated in Table 2.
3.2 Empirical models
3.2.1 Spatial autocorrelation test
We use spatial autocorrelation statistics to test the assumption that the price of univer-
sities can be influenced by neighboring competitors. If the spatial autocorrelation is sig-
nificant, it means that there is strategic interaction in price choice among those
neighboring universities (Ghosh 2010; McMillen, Singell and Waddell 2007).
Spatial autocorrelation statistics measure and analyze the degree of dependency
among observations in a geographic space (Moran 1950). In this study, we use
Moran’sIto test the spatial price interaction of universities in USA. For a row-standar-
dized spatial weight matrix, Moran’sIcan be expressed as:
I=N
ijwij
ijwij(Xi−X)(Xj−X)
i(Xi−X)2,(1)
where Nis the number of spatial units indexed by iand j;Xis the variable of inter-
est; Xis the mean of X; and wij is a matrix of spatial weights. Negative (positive) values
indicate negative (positive) spatial autocorrelation. Values range from −1 (indicating
perfect dispersion) to +1 (perfect correlation). A zero value indicates a random
spatial pattern.
Table 2. Summary of variables.
Subsample (N= 99)
Mean SD
Dependent variable
Difference of tuition and fees in 2008–2009 6806.95 (7875.86)
Independent variables
Distance (1000 miles) 1.10 (1.07)
Undergraduate enrollment (person) 14644.87 (10180.98)
Type (1 = private and 0 = public) 0.54 (0.50)
Graduation rate in four years (%) 60.59 (19.11)
Student finance aid rate (%) 73.15 (13.58)
Ranking 50.5 (20.01)
Student-to-faculty ratio 14.51 (4.52)
Total undergraduate admissions (%) 47.04 (21.12)
Studies in Higher Education 257

A spatial weight matrix is one way of imposing the required structure on the study
of spatial autocorrelation (Getis, Mur and Zoller 2004). This is an N×Npositive and
symmetric matrix which exogenously determines for each observation (row) which
locations (columns) belong in its neighborhood. To study the strategic price behavior
of neighboring universities, we construct two kinds of weight matrixes including con-
tiguity-based spatial weights and k-nearest neighbor spatial weights to describe the
relationship between universities. To the contiguity-based spatial weights, weights
are defined:
wij =1ifj=iand unit jis a “neighbor”of unit i.
wij =0 otherwise.
To the k-nearest neighbor spatial weights, weights are defined:
wij =1ifj=iand unit jis within the k-nearest neighbor of unit i.
wij =0 otherwise.
3.2.2 Spatial regression models
Although the OLS (Ordinary Least Square) regression model without spatial effect may
face the risk of spurious regression, we first use this model as a reference to estimate the
price because in the spatial econometrics literature it is common to start with an OLS
model and use the residuals from that model to test against spatial alternatives. For-
mally, the OLS model is defined as:
Y=
a
+X
b
+1,(2)
where Yis N× 1 of observations which indicate the differences of tuition and fees in
the 2008–2009 school year between the target universities and Harvard University, Xis
an N× 9 matrix of explanatory variables including the distance, the square of distance,
type, graduation rate in four years, student finance aid rate, ranking, student-to-faculty
ratio and total undergraduate admissions, 1is a vector of errors,
b
is the vector of
regression parameters and
a
is the intercept parameter. Nis 99 in the subsample.
Incorporating spatial effects into the model presented earlier gives the following
spatial lag model (SLM) and spatial error model (SEM) (Getis, Mur and Zoller
2004; Anselin 1988).
Formally, SLM is defined as:
Y=
a
+
r
WY +X
b
+1,(3)
where WY is the spatially lagged dependent variable and ρis the spatial autoregres-
sive parameter. In the time-series context, if there is no serial correlation in the errors,
1t, there will be no correlation between yt−1and 1tand OLS will be a consistent esti-
mator. In contrast, (WY )iis always correlated with both 1iand the error term at all other
locations. Hence, OLS is not consistent for SLM and either a maximum likelihood or
instrumental variables estimator is needed.
258 J. Gu

In contrast to SLM, SEM is defined as:
Y=
a
+X
b
+1and 1=
l
W1+
m
,(4)
where
l
is the spatial autoregressive coefwficient,
m
is a vector of errors that are
assumed to be independently and identically distributed and the other variables and par-
ameters are as defined in equation (2). In this model, the error for one observation
depends on a weighted average of the errors for neighboring observations, with
l
measuring the strength of this relationship.
4. Results
4.1 Spatial autocorrelation and strategic interaction
The empirical spatial PD is a widely employed metaphor for problems acted with the
evolution of strategic interaction. In spatial evolutionary game theory, this strategic
interaction relationship between players is not tested, silently assuming that it is signifi-
cant. It is misleading when the analysis frame is used to explain some social behaviors
because not all strategic interactions are significant in reality. In this study, if there is no
significant strategic relationship in pricing process among neighboring universities, it is
deceptive to investigate price behaviors of universities by continuous spatial PD.
As an empirical test, we use the Moran’sItest to assess the degree of strategic inter-
action among neighboring universities by judging the significance of spatial autocorre-
lation (Ghosh 2010; Moran 1950).We compute the Moran’sIof tuition and fees, room
and board and total expenses in 2006–2007, 2007–2008, 2007–2009 and 2009–2010
school years. We first use queen contiguity-based spatial weights to compute
Moran’sI. A queen weights matrix defines a location’s neighbors as those with
either a shared border or vertex (in contrast to a rook weights matrix, which only
includes shared borders). Meanwhile, we also construct k-nearest neighbor spatial
weights to assess the degree of strategic interaction. Neighbor relationship is con-
structed so that each university is assessed within the spatial context of a fixed
number of its closest neighbors. If k (the number of neighbors) is 7, then the seven
closest neighbors to the target university will be included in computations for that uni-
versity. An advantage to this model of spatial relationships is that it ensures there will be
some neighbors for every target university, even when university densities vary widely
across the study area. Here k = 2, 4 and 7, and the results are illustrated in Table 3.
By queen contiguity-based spatial weights, all prices are significant (p< .05), with
tuition and fees in 2009–2010, room and board in 2006–2010 and total expenses in
2008–2009 and 2009–2010 more significant (p< .01). By k-nearest neighbor spatial
weights, all tuition and fees in different school years are significant but the degree of
significance is different for different values of k (p< .1 when k = 2; p< .05 when k
= 4; and p< .01 when k = 7). Total expenses have similar features, but p< .01
when k = 4. For all the weights, room and board in all the four school years are signifi-
cant (p< .01). It is obvious that the prices of universities in this study are significant
strategic interactions between neighboring universities.
The assumption of spatial game theory can be supported by empirical Moran’sI
tests. The test results in Table 3 support the theory of spatial pricing game of univer-
sities. Further, we believe this finding is robust, because the pricing process of
Studies in Higher Education 259

universities is consistently significant for several different sets of spatial weights (i.e. k
= 2, k = 4, and k = 7 closest neighbors) and queen contiguity-based spatial weights.
We ask whether this test and results are robust. For example, what we observe as
autocorrelation might be partially due to the fact that market characteristics (for
example reputation) are also correlated spatially (neighboring Higher Education Insti-
tute experience similar market conditions). Our primary concern here is whether we
have omitted important characteristics such as reputation that cause the spatial autocor-
relation and that, as a consequence, we have overstated the contribution of spatial factor
in higher education competition. To test this assumption, we use regression models to
simulate the price behavior of universities in a spatial game in 2009–2010. The depen-
dent variables are tuition and fees, room and board, and total expenses, respectively.
The independent variable is the ranking number. Each university has a ranking
number from 1 to 100. The smaller this ranking number is, the higher the university
ranks. Here we use it as a reputational variable. Those three models include OLS
model, SLM with queen contiguity-based spatial weights, and SEM with queen conti-
guity-based spatial weights. The estimated coefficients are illustrated in Table 4.
Table 4. Moran’Itest of price in 2009–2010.
a
OLS SLM SEM
Reputation
coefficient
Reputation
coefficient
Spatial factor
coefficient
Reputation
coefficient
Spatial factor
coefficient
Tuition and fees –169.933*** –164.467*** 0.235* –163.44*** 0.232*
Room and board –26.197*** –21.449*** 0.433*** –18.727*** 0.414***
Total expenses –184.585*** –176.815*** 0.262** –174.786*** 0.243*
a
For tuition and fees, R
2
= .372, .399 and .389 in OLS, SLM and SEM models, respectively. For room and
board, R
2
= .164, .301 and .271 in OLS, SLM and SEM model, respectively. For total expenses, R
2
= .333,
.37 and .356 in OLS, SLM and SEM model, respectively.
*p< .1; **p< .05; ***p< .01.
Table 3. Moran’sItest of price.
Year
Queen
contiguity-
based spatial
weights
k-nearest
neighbor spatial
weights (k = 2)
k-nearest
neighbor spatial
weights (k = 4)
k-nearest
neighbor spatial
weights (k = 7)
Tuition and
fees
2006–07 0.1346** 0.1262* 0.1566** 0.1655***
2007–08 0.1269** 0.1216* 0.1502** 0.1615***
2008–09 0.1417** 0.1353* 0.1506** 0.1602***
2009–10 0.1478*** 0.1256* 0.1482** 0.1542***
Room and
board
2006–07 0.3162*** 0.3119*** 0.3364*** 0.3340***
2007–08 0.3215*** 0.3351*** 0.3630*** 0.3434***
2008–09 0.3270*** 0.3328*** 0.3521*** 0.3329***
2009–10 0.3152*** 0.3006*** 0.3211*** 0.3113***
Total
expenses
2006–07 0.1475** 0.1182* 0.1712*** 0.1725***
2007–08 0.1414** 0.1208* 0.1754*** 0.1723***
2008–09 0.1661*** 0.1359* 0.1795*** 0.1748***
2009–10 0.1723*** 0.1316* 0.1788*** 0.1704***
*p< .1; **p< .05; ***p< .01.
260 J. Gu

As illustrated in Table 4, if all other variables are controlled, all the coefficients of
reputation are statistically significant and they all are negative. The results are consist-
ent with the literature in this field. Universities with better reputation set higher prices.
Not surprisingly, the coefficients of spatial factor in SLM and in SEM are statistically
significant. This empirical evidences support the argument of Haveman and Nonne-
maker (2000). Two universities will compete at the same time on multiple market seg-
ments with a different spatial reach, e.g. competing for bachelor students at the regional
level, while competing for academic reputation at the international level.
Here we still do not know to which extent socio-demographical characteristics of
neighborhoods might account for the observed spatial autocorrelation; however, the
average effect of spatial factor with statistically significant neighborhood similarity
for all prices is generally 0.3 (the average of all spatial factor coefficients in Table
4). This is a conservative estimate which implies that less than 70% of the observed
spatial autocorrelation is due to other contextual factors. It shows that spatial neighbor-
hood does matter when universities set their prices.
4.2 Neighborhood size and equilibrium choice
According to the empirical spatial PD, an important insight is that spatial structure can
promote persistence of cooperation. In particular, if the PD is played in spatially struc-
tured populations, in which individuals interact only within a limited local neighbor-
hood, then cooperation can be maintained. Conventional antitrust wisdom asserts
that the relative size of firms does matter, while Robert Axelrod’s(1997) analysis
cannot inform us if this conventional wisdom is correct because the tournaments
took no account of varying neighborhood size in a spatial game. For the antitrust
context, conventional wisdom implicitly acknowledges the possibility of effects of
neighborhood size on equilibrium but is agnostic about the extent of its impact. Here
we investigate the effects of spatial structure on the pricing game of higher education.
Three simulations will be performed to investigate the effects of neighborhood size and
those evidences are crucial to the analysis of tacit cartel collusion in the higher edu-
cation field.
4.2.1 Neighborhood size and reciprocal cooperation
First, we want to investigate the effects of increasing neighborhood size on the fre-
quency of strategic interaction. We compute Moran’sIvalues of all prices including
tuition fees, room and board and total expenses in the 2008–2009 school year with
k-nearest neighbor spatial weights (k = 1, 2, …, 30), which are illustrated in Figure
1. Moran’sIvalue is not a direct indicator measuring the degree of reciprocal altruism,
however, it can measure the interaction intensiveness and frequency among players in a
spatial game, which reflects the predisposition to reciprocal altruism because players
with more intensive and frequent interactions are more likely to show altruism (Rotem-
berg 2008; Fletcher and Zwick 2007), and are more likely to form some kind of collu-
sion. Experimental control is particularly useful because game theory predictions often
depend sensitively on the choices players have, how they value outcomes, what they
know, the order in which they move, and so forth. In this part, we want to investigate
to what degree the strategic interactive behavior in a spatial game is sensitive to the
neighborhood size, one detail of the game environment. So we control all factors
except the number of neighboring competitors.
Studies in Higher Education 261

Generally, the Moran’sIvalue decreases as the neighborhood size increases, undu-
lately and cyclically. All the Moran’sIvalues are significant at p< .05, except the
tuition and fees and total expenses with k = 1, which are significant at p< .1. This is
robust evidence that proves the effect of neighborhood size on the pricing game of uni-
versities. In this spatial pricing game, the payoff of every university depends on the
reaction functions of its neighboring universities. When the neighborhood size is
small, e.g. the number of neighbors is less than 11, it is possible for a university to
identify all neighbors’reaction functions and to determine the payoffs of the mix of
neighbors’strategies.
4
As a result, the strategic interaction is intense and the average
Moran’sIvalue is high. As the neighborhood size increases to more than 11, the
spatial structure will become more complex and it becomes a complex network that
affect the payoff of the price game. As the neighborhood increases, the space of the
price game also extends and the strategic interaction will be relatively covert.
The implications for antitrust in higher education are subversive. The results
suggest that law could permit universities to share information or take part in regular
meetings until there are few neighboring competitors remaining in the market. As illus-
trated in Figure 1, when the neighboring competitors are fewer than 11, the strategic
interactions among them are intensive. In this situation it is more likely for those uni-
versities to form reciprocal cooperation, including price fixing, which might reduce the
benefit to the public. In other words, universities with few neighboring competitors are
more likely to show altruistic behavior with a strong predisposition to cooperate with
others and to punish those who violate the norms of cooperation (Henrich et al.
2001). As long as there are many neighboring competitors, the game’s logic suggests
that even highly organized groups would encounter the same inability to achieve coop-
erative prices because of high transaction cost. This implies that when there are many
neighboring competitors, universities have no incentive to collude and antitrust cam-
paign in higher education might be redundant.
However, the available empirical evidence on the link between multimarket contact
and spatial interaction is not totally conclusive in higher education. Whereas the
Figure 1. The relationship between neighborhood size and Moran’sI.
262 J. Gu

theoretical arguments tend to suggest a positive link between multipoint competition
and the incentives of firms to be tolerant with neighboring rivals, the empirical tests per-
formed offer no significant results (Greve and Mitsuhashi 2004). We use reputational
variables such as ranking number to describe multipoint completion and compute
bivariate Moran’sIbetween price and reputational variable in nearby universities.
5
Bivariate Moran’sIvalues of those variables in the 2008–2009 school year with k-
nearest neighbor spatial weights (k = 1, 2, …, 30) are computed and all are negative.
The absolute value of bivariate Moran’sIvalues are illustrated in Figure 2.
The bivariate Moran’sIvalues are negative, which means that a university in proxi-
mity to lower-ranking universities (higher numbers) are much more likely to set a lower
price. Behind the phenomenon lies the spread and intensification of what Robert
H. Frank (2001) called “winner-take-all markets”in higher education. In the
“winner-take-all market”context, how can higher education institutes with fewer
resources compete with elite universities? It is unwise for them to compete with elite
universities directly. Most institutes neighboring lower-ranking universities set low
prices to optimize their position in the local higher education market. However,
when there are more than neighbors, the absolute value of bivariate Moran’sIwill
be less than .1. This implies that the diffusion of reputation helps in the further
buildup of “cooperative local network”in the pricing game among neighboring univer-
sities, while the effect of reputation on price can be diluted when more neighbors take
part in the pricing game.
4.2.2 Neighborhood size and strategies
Second, we investigate the effects of neighborhood size on observed strategies includ-
ing cooperation and defeat. In spatial PD, there are two price strategies that every
Figure 2. Absolute values of bivariate Moran’sIbetween price and reputation.
Studies in Higher Education 263

university can choose, high price or low price. Considering its neighbors’prices, each
university has four price strategies to play. If its neighbors choose a high price, the uni-
versity can choose the cooperation solution and choose a high price as well (HH). The
university can also choose the defeat solution and choose a low price (HL). If its neigh-
bors choose a low price, the university can choose the cooperation solution and choose
a low price as well (LL). The university can also choose the defeat solution and choose
a high price (LH). So in this game, the cooperation solution of Nash equilibrium
includes HH and LL, while the defeat solution includes HL and LH. In the spatial
price game of universities, some universities may stay neutral so the strategic inter-
action between their neighbors is not significant. We use the LISA (Local Indicators
of Spatial Association) test to identify how many universities use each strategy in
different k-nearest neighbor spatial weights (k = 1, 2, …, 30) (Anselin et al. 2004).
Because there are 100 universities in this sample, the possibility of each Nash equili-
brium is equal to the number of the universities choosing the strategy. For example,
if five universities choose the HH strategy in this game, the possibility of the HH sol-
ution is 5%.Similarly, the possibility of cooperation Nash equilibrium is equal to the
sum of HH and LL, while the possibility of defeat Nash equilibrium is equal to the
sum of HL and LH.
As illustrated in Figure 3, the possibility of cooperation Nash equilibrium depends
significantly on the neighborhood size. There are three stages. If the neighborhood size
is less than 5, the possibility of cooperation increases quickly as the neighborhood size
expands. Then the possibility tends to stability until the neighborhood size achieves
25, after which there is an increasing trend. The result of the second stage is striking.
There is a long-term relatively stable cooperation when the neighborhood size is
between 5 and 25.
6
The implication for antitrust in higher education is illuminating. Skep-
ticism about antitrust in higher education is widespread. As Frank (2001) argued, “Ani-
mated by its belief that unbridled competition always and everywhere leads to the best
outcome, the Justice Department took a dim view of this agreement. And it brought an
antitrust suit that led to its termination.”Yet analysis of spatial PD concisely and compel-
lingly formulates admiration of the antitrust doctrine’sconfidence that tacit collusion and
cooperation are likely evolve from a repeated prisoner’s dilemma context. Once a kind of
Figure 3. The effect of neighborhood size on the cooperation solution.
264 J. Gu

collusion has been formulated in higher education, it is hard to terminate it without anti-
trust intervention, even in a spatial game with increasing neighborhood size.
Generally, the possibility of defeat increases as the neighborhood size expands, as
illustrated in Figure 4. In spatial PD, the universities who choose defeat behavior will
face tit-for-tat competition if the defeat behavior is detected by other competitors. So
universities with the defeat strategy need to test the reaction of neighbors by adjusting
their defeat behavior. If the neighborhood size is more than 10, the possibility of defeat
increases directly because the result of defeat can be diluted by numerous players. This
result is thought-provoking. Even a highly organized group would encounter the same
inability to avoid the defeat solution due to information dissymmetry. This implication
contradicts the court’s confidence that data exchanges in higher education ought to be
illegal because it is so easy to persuade competitors –even in large numbers –to do
“that which will obviously prove profitable”. In fact, it is increasing difficult to form
collusion as the neighborhood size increases and defeat is always a possible strategy
for some universities because of their characters. For example, in 2002 Brown, Prince-
ton, Harvard, Stanford, and Yale Universities all derogated the two explicit agreements
to which large numbers of colleges have committed themselves: the guidelines of
NACAC and the College Board, which closely resembled a threatened defection
from a cartel in higher education. The spatial price game suggests that the success of
a cartel in higher education is contingent upon the conformity of its members with
agreed conditions. Defection, or “cheating,”is always a threat, because it rewards
the defector, at least temporarily, with greater benefits.
4.2.3 Neighboring size and equilibrium
Third, we will investigate the effects of neighborhood size on Nash equilibrium. In
spatial PD, the non-cooperative state is evolutionarily stable, which has inspired numer-
ous investigations into the extensions that enable cooperative behavior to persist. In
particular, on the basis of spatial extensions of PD, it is widely accepted that a
spatial structure promotes the evolution of cooperation (Clemens and Riechmann
2006; Kirchkamp 2000; Killingback and Doebeli 1996; Nowak and May 1992).
Figure 4. The effect of neighborhood size on the defeat solution.
Studies in Higher Education 265

However, Hauert and Doebeli (2004) found that a spatial structure often inhibits the
evolution of cooperation in the snowdrift game. There are few empirical tests of
these opinions, which makes the argument misleading because both advocator and
opponent lack empirical evidence. In this study, we want to predict the long-term
Nash equilibrium in different neighborhood sizes. In the long term, what is the possi-
bility of cooperation or defeat in spatial price game of universities with different neigh-
borhood sizes? To answer this question, we compute the C/D rate (the percentage of
cooperation divided by the percentage of defeat), as illustrated in Figure 5.
As the neighborhood size expands, the C/D rate fluctuates, which shows that spatial
structure affects Nash equilibrium directly. The highest value of C/D rate is 6 with six
neighbors, so the C/D rate has an upper limit which means spatial structure cannot com-
pletely eliminate defeat, because defeat is also an endogenous equilibrium of the spatial
price game of universities in this spatial PD. The lowest value of C/D rate is 1.5 with
one neighbor, which means cooperation is the dominant strategy and equilibrium in this
game, which is predicted by evolutionary game theory (Clemens and Riechmann 2006;
Nowak and May 1992). In the long term, the C/D rate converges to 3.22 (the average of
C/D rates), which shows that the possibility of cooperation equilibrium is 76% and the
possibility of defeat equilibrium is 24%.
The PD illustrates that cooperating individuals are prone to exploitation, and that
natural selection should favor cheaters (Hauert and Doebeli 2004). However, our
results show that universities prefer the cooperation strategy than the defeat strategy.
The implication for antitrust in higher education is that the existence of direct recipro-
city in a group of universities will induce the evolution of generalized reciprocity,
entailing much higher levels of cooperation overall. For example, the cooperation
among the eight Ivy League colleges give a good demonstration for the “Pentagonal/
Sisters group”including Amherst, Barnard, Bowdoin, Bryn Mawr, Colby, Mount
Holyoke, Middlebury, Smith, Trinity, Tufts, Vassar, Wesleyan, and Williams. Here
the truth of the 1991 antitrust campaign emerges. Though there is no strong evidence
to support the price-fixing collusion among the Ivy League group, it is very possible
that such overt cooperation will spread over the higher education field and more and
more higher education institutes will form similar groups to achieve the benefitof
Figure 5. The effect of neighborhood size on Nash equilibrium.
266 J. Gu

collective behavior. As a result, some will use contrivance or conspiracy to reduce the
benefits to the public as Adam Smith (1776) had suspected. The Justice Department just
took certain actions so as to warn others in the higher education field. This does not, of
course, mean that the mere existence of possible collusion in higher education is suffi-
ciently important to give the antitrust authorities enough ground to take suitable legal
actions against such potential infringement. However, without this kind of antitrust
campaign, it is difficult to let those in academia realize that there is a potential threat
to the public if higher education institutes choose some collective actions. It’s naive
to consider higher education institutes as only nonprofit institutions involved in edu-
cation, not commodities. The courts clearly have stated that the antitrust laws, and
the per se rule, govern all markets that have not been specifically exempted by Con-
gress. In this way, the antitrust campaign has been successful. After the great shock,
more and more people in academia realize that it is necessary for higher education
institutes to maintain a competitive landscape.
One issue that has puzzled observers is how a collusive equilibrium, if it exists,
could be maintained in higher education. The puzzle arises because higher education
has many institutes with long histories, even within (most) metropolitan areas. Econ-
omic theory suggests that the difficulty of sustaining collusion grows with the
number of actors (Tirole 1988) and this has been borne out in experimental studies
(Valerie and Mark 1984). The results suggest that higher education institutes may
wish to maintain a climate of cooperation with their counterparts. In doing so, they
might engage in retaliatory tactics if a peer fails to maintain this climate of cooperation.
Retaliatory sanctions are a principal, hallmark means of enforcement of agreement
among cartel members in higher education. It is the potential reason why Harvard
chose in the end to abide by the agreement just one month after its defection from
the guidelines of NACAC and the College Board in June 2002. In the Ivy Overlap
Group all members understand that failing to comply with the Overlap Agreement
will result in retaliatory sanctions. Consequently, noncompliance is rare and quickly
remedied. The results imply that retaliation is likely to lead to reciprocity among com-
petitive higher education institutes because cooperation can benefit all members in the
long run. Any readers who doubt the potential collusion in higher education should ask
themselves why NACAC and the College Board exert influence over their members to
uphold the agreement among colleges.
Table 5 presents empirical evidence to check the robustness of the above tests. What
are the effects of increasing national competition in local markets in higher education?
We investigate the effects of reputation competition at the national level on the outputs
of the local spatial game. The correlation coefficients between those outputs and
Moran’sIvalues of the reputational variable in the 2008–2009 school year with k-
nearest neighbor spatial weights (k = 1, 2, …, 30) are computed in Table 5.
7
Table 5. The correlation coefficient between Moran’sIvalues.
Ranking number
Cooperation rate –0.696**
Defeat rate –0.699**
C/D rate 0.493**
Note: correlation is significant at the .01 level (2-tailed); ** significant
at 5%.
Studies in Higher Education 267

Both the cooperation rate and defeat rate are significantly negative to Moran’sIof
reputational variables. This shows that an increase in reputation diffusion at the national
level can reduce cooperation rate and defeat rate as well at the local level, but increase
C/D rate due to the positive correlation coefficient between C/D rate and Moran’sIof
reputational variable. The relatively higher C/D rate is a possible consequence of repu-
tation effects. These findings are in line with those of Greve and Mitsuhashi (2004)who
argue that reputation effects generally lead to higher, more extreme outcomes and
organizations with multimarket contact are more likely to collaborate on their activities.
Our results support the argument that increasing national competition unequivocally
restrains market power in local markets, leading to a low likelihood of equilibrium
in a spatial game (Anderson and De Palma 2000). Moreover, our results also indicate
that cooperation still dominates defeat in the spatial game when taking into account
reputation competition at the national level (Roca, Cuesta and Sánchez 2009).
4.3 Price fixing or not
It has been believed that price fixing is so strongly productive of anticompetitive effects
that to launch inquiries into its reasonableness would be wasteful of judicial resources.
If the courts apply a per se rule of illegality to price fixing in higher education, it denies
any opportunity for defendants’rebuttal. However, whether it is proper to apply a per se
rule to cooperation among higher education institutes is intensely controversial. Dedu-
cing from the spatial pricing game, if there is overt or covert price fixing among higher
education institutes, the price difference among them is insensitive to the characters of
universities. In other words, if there is tacit collusion in setting price, higher education
institutes will charge substantially similar “sticker prices”for tuition, room, board, and
fees, regardless of their setting. In empirical research, we can detect possible tacit col-
lusion by testing the existence of sticker prices. In higher education, “sticker prices”
means that price differences are sensitive to distance among universities and among
some neighboring universities there is at least one university serving as a price bench-
mark, while the prices of neighboring universities stick to the price of the benchmark.
To test this assumption, we use three models to simulate the price behavior of uni-
versities in the spatial game. The three models include OLS (second column of Table
6), SLM with queen contiguity-based spatial weights (third column) and SEM with
queen contiguity-based spatial weights (fourth column). The dependent variable is
the difference of tuition and fees in 2008–2009 between Harvard University and
other universities. The variable name is DOP. We also compute the arc distance
between Harvard University and other universities and the variable name is D1.
8
The
square of D1 is D2. The variable name of undergraduate enrollment is UNDERG.
TYPE is the type of university –private or public. 4GRATE is the percentage of
full-time, first-time students who graduated in four years. PGRANT means percentage
of students receiving any financial aid. Ranking is the ranking number from the US
News ranking system. STOF is student-to-faculty ratio and TNADM is total under-
graduate admissions. We exclude Harvard University in this sample because Harvard
University is a benchmark in this empirical research, so the number of units in this
sample is 99.
A robustness check is conducted here to investigate whether our results are plaus-
ible. We want to examine how certain “core”regression coefficient estimates behave
when the regression specification is modified by dropping some independent variables.
We drop STOF and TNADM in another three models in Table 6. These three models
268 J. Gu

Table 6. Results of regression.
DOP DOP
Variable OLS SLM(W1) SLM(W1) OLS SLM(W1) SEM(W1)
CONSTANT 422.72 (0.088) 229.41 (0.05) 160.83 (0.038) –1509.044 (–0.323) –1450.209 (–0.318) –1269.745 (–0.303)
D1 3341.13 (2.127)** 3149.05 (1.858)* 3043.41 (2.703)*** 3258.822 (2.083)** 3310.592 (1.921)* 2943.036 (2.625)***
D2 –1245.82 (–2.781)*** –1196.06 (–2.256)** –1177.36 (–3.543)*** –1248.96 (–2.813)*** –1196.06 (–2.631)*** –1162.499 (–3.538)***
UNDERG –0.23 (–1.997)** –0.22 (–2.048)** –0.24 (–2.376)** –0.268 (–2.382)** –0.269 (–2.475)** –0.268 (–2.696)***
TYPE 7582.32 (5.407)*** 7541.88 (5.666)*** 8361.69 (6.559)*** 6919.389 (5.314)*** 6930.317 (5.544)*** 7814.451 (6.686)***
4GRATE –99.916 (–2.224)** –98.361 (–2.297)** –113.15 (–2.847)*** –93.347 (–2.081)** –93.82 (–2.165)** –107.089 (–2.689)***
PGRANT 1.68 (3.378)*** 1.67 (3.541)*** 1.56 (3.546)*** 1.699 (3.478)*** 1.699 (3.625)*** 1.589 (3.629)***
Ranking 84.64 (2.826)*** 86.18 (3.001)*** 72.74 (2.745)*** 56.048 (2.231)** 55.818 (2.303)** 49.643 (2.209)**
STOF –154.05 (–0.916) –152.59 (–0.954) –95.63 (–0.617)
TNADM –49.739 (–1.474) –51.52 (–1.584) –44.42 (–1.48)
ρ0.027 (0.245) –0.007 (–0.063)
l
–0.44 (–2.534)** –0.449 (–2.615)***
R
2
0.739 0.74 0.76 0.739 0.73 0.75
Log
likelihood
–962.07 –962.04 –959.73 –962.07 –963.707 –961.018
AIC 1944.14 1946.08 1939.46 1944.14 1945.41 1938.04
SC 1970.09 1974.62 1965.41 1970.09 1968.77 1958.8
Breusch-
Pagan test
142.59*** 142.583*** 135.98*** 142.59*** 111.205*** 105.457***
LM (lag) 0.173 0.062
LM (error) 5.318** 2.991*
*p< .1; **p< .05; ***p< .01.
Studies in Higher Education 269

include OLS (fifth column), SLM with queen contiguity-based spatial weights (sixth
column), and SEM with queen contiguity-based spatial weights (seventh column).
Model selection is important in spatial analysis. As illustrated in Table 6,the
Lagrange multiplier (lag) is insignificant while Lagrange multiplier (error) is significant,
which means that SEM is better than SLM. According to the R
2
value, SEM with queen
contiguity-based spatial weights is the best, which is confirmed by the log likelihood test,
Akaike information criterion (AIC) test and Schwarz criterion (SC) test. As a result, we
choose SEM with queen contiguity-based spatial weights (fourth column) as the main
model in our analysis, and other models as reference.
9
Crawford (1997)argued,“Behav-
ior in games is notoriously sensitive to details of the environment, so that strategic models
carry a heavy informational burden, which is often compounded in the field by an
inability to observe all relevant variables.”We control the experiment by two aspects
including student-to-faculty ratio and total undergraduate admissions. The empirical
results show that all those variables are insignificant, which means the experimental con-
trolling technique runs well. This gives the spatial price game experiments a decisive
advantage in achieving robust results which are unlikely to be less reliable than casual
empiricism or introspection, as Crawford (1997)said.
The empirical result shows that the difference of price is positively related with dis-
tance and negatively related with the square of distance when Harvard University is the
benchmark, which means that the relationship between the difference of price and the
distance is an inverse U-shaped curve. The difference of price will increase as the dis-
tance increase, which means that neighbors are more likely to use the cooperation strat-
egy than remote universities in a spatial game. So neighbors will choose similar prices
to keep cooperation Nash equilibrium because the payoff of cooperation is better than
defeat and the difference of price is minimal. However, as the distance increases to a
threshold, the neighborhood relationship will change and a new group of neighbors
will appear. A new cooperation Nash equilibrium will form in this spatial game. For
example, in the west, Stanford University will be a new benchmark in the west area
and the difference of prices between Stanford University and Harvard University is
small though the distance between those two universities is large.
It is reasonable that there is an umbrella effect behind the inverse U-shaped curve in
the spatial price game of higher education. In a neighborhood area, there is a bench-
marking university whose price has a guidance function and within the umbrella area
the prices of neighbors are similar because the cooperation Nash equilibrium is the
dominant strategy. Meanwhile, outside the umbrella area, the difference of price will
increase as the distance increases. Then there is another umbrella area and neighbor-
hood group. The two umbrella areas may be remote while the difference of equilibrium
prices may be small. Hoxby (1997) and McMillen, Singell and Waddell (2007) discov-
ered that the US higher educational system had been transformed from a collection of
local, independent college fiefdoms into a regionally and nationally integrated market
in which universities competed for both resources and students, but these authors did
not explain the competitive behaviors of universities in regional and national
markets. Here, the umbrella effect in the spatial price game of higher education indi-
cates the strategic behaviors in regional and national market.
The “sticker prices”phenomenon of higher education is also confirmed by the
results that the difference of price is sensitive to some characters of universities. The
difference of prices is negatively related to undergraduate enrollment of universities
(p< .01) and the percentage of full-time, first-time students who graduated in four
years (p< .01), while is positively related to the type of universities (p< .01) and
270 J. Gu

the percentage of students receiving any financial aid (p< .01). Though behavior in
games is sensitive to details of environment, we can also find some clues from the com-
plicit dynamics of games. The empirical results show that the scale of universities and
graduation rate can affect the difference of prices negatively, which means larger uni-
versities are more likely to implement the cooperation strategy as well as universities
with higher graduation rates. The type of university and the rate of receiving financial
aid affect the difference of prices positively, which means private universities are more
likely defeat the public universities.
The results show that the difference of price is sensitive to both distance and char-
acters of universities, and where this is true the analysis of this paper has detected the
existence of sticker prices in higher education. Where both occur, however, and without
antitrust intervention higher education institutes are apt to tacit collusion. Under this
situation, higher education institutes line up commitments before issuing financial
aid packages, and they respect each other’s commitments by declining to compete
for them. As Henry (2005) argued, “Facing no competition from market peers, these
colleges enjoy the equivalent of exclusive bargaining rights. They are free, and safe,
in offering less-generous financial aid packages than they would on the open market.
Indeed, they have every incentive to do just so, as rational maximizers of their own uti-
lities”(Henry 2005, 876). This does not mean that the mere existence of the sticker
prices phenomenon is sufficient to justify an antitrust campaign in higher education.
But since a relatively significant spatial affiliation in price of universities usually
requires collective actions, the existence of a sticker prices phenomenon of this magni-
tude is sufficiently important to give the antitrust authorities pause before rejecting alle-
gations of tacit collusion in higher education.
Table 6 shows that all the coefficients of ranking are significant, indicating that the
effect of reputation on the local pricing competition in higher education is important.
Our results show that spatial interaction is a reasonable component of a complete
status competition model, in which reputation also plays its role.
To test the sticker prices phenomenon in the higher education field and evaluate the
umbrella effect, it’s important to bring a penetrating analysis of the relationship
between higher education institutes’optimal pricing behavior and spatial scale. To do
this, two competition scenes are constructed. The first is that every university competes
with 99 other universities in the USA, which can be labeled “national competition”.
This weight matrix is constructed using 99 nearest neighbors for each university. The
second is that every university competes with its four nearby competitors, which can
be labeled “regional competition”. This weight matrix is constructed using four nearest
neighbors for each university (Ghosh 2010). Here, we use the LISA test again to test
the sticker prices phenomenon based on the umbrella effect by drawing a comparison
between two pricing behaviors at different spatial scales (Anselin et al. 2004). The
sticker prices theory based on the umbrella effect claims that universities have more
pricing diversity at a local scale than at the national scale. The pricing results are
pooled in Table 7, where HH, LL, LH, and HL have the same definitions as before and
NON means there is no significant spatial autocorrelation between nearby universities.
As illustrated in Table 7, there is no HH pricing behavior and also LL pricing be-
havior can be ignored at the national scale. Only tuition and fees from 2006 to 2009
have 3% LL type of pricing behavior at national scale. At the national scale, almost
all pricing behaviors are concentrated to LH and HL types if there is spatial autocorre-
lation between nearby universities. However, there are four types of pricing behavior at
local scale. HH and LL types of pricing behavior occupy a dominant position, while LH
Studies in Higher Education 271

and HL types of pricing behavior cannot be ignored. So the empirical results show that
there is more pricing diversity at a local scale than at the national scale.
Pricing diversity is used to test the idea that competition structure in higher edu-
cation is non-random, with structurally complex price stickers at a local scale support-
ing more pricing behaviors with more competitive diversity than simple price stickers at
the national scale. Because of the umbrella effect, patterns of competition of univer-
sities in a local area are principally driven by regional price stickers acting as environ-
mental filters. As a result, structurally complex price stickers in a local area can
facilitate coexistence of competitors.
5. Discussion and conclusion
As Wiley (1988) argued, “Until that theory can give judges helpful generalizations
about when cooperation is more likely than competition, antitrust will continue to be
based only on the current fashion in guesswork”(Wiley 1998, 1928). The criticism
of price collusion in higher education never stops (Stilwell 2003; Mitten 1995; Morri-
son 1992). In this study, we prefer empirical research to normative research, and to
investigate the price behavior of universities rather to give a normative judgment of
those behaviors. Especially, we focus on questions of why universities prefer
cooperation to defeat and how spatial factors such as neighborhood and geographical
distance affect the price behaviors of competitive universities. We target the top 100
universities in USA to analyze the price behavior of colleges in spatial game frame.
Using data from the National Center for Education Statistics (NCES), we inferred a
number of interesting empirical results.
5.1 List of interesting results
First, spatial autocorrelation is significant and spatial interactions play a prominent role
in understanding the price behaviors of universities (Ghosh 2010; Black 2001). By
testing the price variables including tuition and fees, room and board and total expenses
Table 7. Price behavior at different competition scales (%).
National competition Regional competition
Year NON HH LL LH HL NON HH LL LH HL
Tuition and fees 2006–07 35 0 3 36 26 69 20 5 3 3
2007–08 41 0 3 32 24 70 20 5 3 2
2008–09 51 0 3 24 22 73 18 5 3 1
2009–10 50 0 0 27 23 73 19 4 2 2
Room and board 2006–07 60 0 0 14 26 71 17 9 1 2
2007–08 63 0 0 8 29 68 20 7 1 4
2008–09 59 0 0 12 29 72 18 4 1 5
2009–10 59 0 0 11 30 78 13 3 1 5
Total expenses 2006–07 52 0 0 17 31 73 16 6 2 3
2007–08 47 0 0 28 25 75 15 5 2 3
2008–09 64 0 0 15 21 74 16 5 2 3
2009–10 37 0 0 26 37 76 14 5 3 2
*p< .1; **p< .05; ***p< .01.
272 J. Gu

in difference school years with different spatial weights, we find robust evidence that
the prices of universities are significantly spatially correlated. So if the spatial factors
are missed, the results will be biased. The study of McMillen, Singell and Waddell
(2007) speaks to the potential importance of enrollment management in college
access by introducing spatial proximity into empirical models of tuition, while our
study shows that the importance of spatial factors is not only potential but also
robust and it is necessary to incorporate it into price model of universities.
Second, the findings of our study provide more empirical support for the strong
version of the mutual forbearance hypothesis between spatial multipoint competitors:
universities interacting in multiple geographical segments of their market are signifi-
cantly more likely to engage in price collaboration. Our results show that the diffusion
of reputation helps in the further build-up of this “cooperative local network”in the
spatial price game among neighboring universities. Our results are qualitatively consist-
ent with, but also go beyond, prior studies of mutual forbearance. We focus almost
exclusively on possible consequences of collaboration induced by competition in mul-
tiple geographical markets. We find that there are three effects boosting cooperation in
triplets of interacting neighboring universities: (i) localized interactions; (ii) reputation
and (iii) other characters of each university. All three effects tend to promote the emer-
gence of cooperation in the spatial price game of higher education.
Third, spatial structure such as neighborhood size can affect the Nash equilibrium in
price game of universities (Ghosh 2010; Millimet and Rangaprasad 2007; Greenbaum
2002). As the neighbor size increases, the cooperation rate and the defeat rate both
increase while the C/D rate will converge to 3.22, which shows the possibility of
cooperation equilibrium is 76% and the possibility of defeat equilibrium is 24%. Our
study confirms the judgment that human society is based to a large extent on mechan-
isms that promote cooperation (Fletcher and Zwick 2007; Clemens and Riechmann
2006; Sanchez and Cuesta 2005).
Fourth, the relation between price and geographical distance of universities is non-
linear, which means the relation is complex and dynamic. Our results show that the
difference of prices is positively related to the distance while negatively related to
the square of distance. So it is an inverse U-shaped curve rather a straight line,
which means that neighbors are more likely to using cooperation strategy than
remote universities in spatial game. However, as the distance increase to a threshold,
the neighborhood relationship changes and a new group of neighbors appears. The
inverse U-shaped curve relation is different to the result of McMillen, Singell and
Waddell (2007)whofind list and net tuition are inversely related to distance
between institutions.
5.2 List of improvements
Given its data and methodological limitations, this study can be improved in several
ways. First, spatial econometrics has its roots in the study of geography, so these appli-
cations have typically used geographic notions of distance in their spatial model speci-
fication. However, there is no inherent reason for why spatial distance should be limited
to geographic distance (Getis, Mur and Zoller 2004). If other distances such as social
distance or economic distance can be used, it can deepen our understanding of the
recruiting competition of universities and give more insight into this issue.
Second, this study used the difference of tuition and fees level as its dependent vari-
able. This is only one of price instruments used by universities (Gowen and Owen
Studies in Higher Education 273

2006). We tried to find other instruments, e.g. net tuition as used by McMillen, Singell
and Waddell (2007). However, because of the missing data, we could not collect those
data. In a following study with better-balanced data, we will conduct separate analyses
for each policy instruments of enrollment strategy of higher education. Moreover, there
are several factors such as student loan policy, government grants, socio-economic
factors and competition between colleges that could affect the college tuition and
fees. Meanwhile, there are many institutional spending factors that contribute to
tuition setting decision including capital construction costs, technological and service
improvements, competition for faculty and students, the growing cost of healthcare
and employee benefits, mission creep, and lack of spending transparency. However,
we cannot test those factors here because those data are unavailable.
Finally, the sample was based on the top 100 universities in the USA. It did not
include all the universities and colleges in the USA due to data collecting difficulties.
These problems may cause sample selection bias. In a future study, we may use a
natural experiment situation induced by government or institutional changes in enroll-
ment policy to identify the strategic interaction association between neighbors.
Acknowledgements
This research was supported by the MOE Project of Key Research Institute of Humanities and
Social Sciences in Universities, Project 2009JJD880002. We are grateful for comments and sug-
gestions by two anonymous referees. Special thanks also go to Professor Vincent Meek. All
remaining errors and omissions are my own.
Notes
1. This study focuses on the empirical investigation of spatial game, and the rationality of
those empirical researches mainly comes from classic spatial evolutionary game models
(Killingback and Doebeli 1996; Nowak and May 1992). In these classic papers, there are
mathematical derivations to explain how cooperation strategy typically evolves in a
spatial evolutionary game, while this research focuses on experimental verification.
2. The methodology of these rankings is illustrated in this page: http://www.usnews.com/
education/best-colleges/articles/2012/09/11/how-us-news-calculates-its-best-colleges-
rankings?page=4.
3. We choose Harvard University as the benchmark because Harvard University is the top uni-
versity on the US News ranking system.
4. As illustrated in Figure 1, the Moran’sIvalues of all prices are larger than .1 when the
number of neighbors is less than 11. When the number of neighbors is more than 11, the
Moran’sIvalues of all prices except room and board are all less than .1. For the curve
of room and board, it is obvious that there are two different patterns before and after
there are 11 neighbors. So it is reasonable to treat 11 as the threshold.
5. A bivariate measure of spatial correlation relates the value of a variable at a location to that
of a different variable at neighboring locations, as a straightforward generalization of the
concept of spatial autocorrelation (Anselin et al. 2005). A bivariate spatial association
measure captures the relationship between two variables, taking the topological relationship
among observations into account. In other words, it parameterizes the bivariate spatial
dependence (Lee 2001).
6. It is well known that cooperation can be favored in this game if players have repeated inter-
actions –such a scenario sets up the possibility of reciprocal cooperation, which implies that
promotion of cooperation is possible on local agents constrained to act in geographical
space when the neighborhood size is not very large. However, the possibility that coopera-
tive strategies drop when the size grows very large cannot be excluded.
7. Moran’sIis similar but not equivalent to a correlation coefficient. Moran’sItests for global
spatial autocorrelation for continuous data. Here we use Moran’sIof reputational variable
274 J. Gu

to measure the spatial interaction intensity with different neighborhood sizes. The corre-
lation test between prices and Moran’sIof reputational variable is used here as a
measure of the strength of linear dependence between price and spatial interaction intensity
of reputation, not reputation. The statistical significance of correlation coefficients between
those variables is a measure of how well the price variables and spatial interaction intensity
of reputation are related.
8. In this section, the unit of arc distance measurement is 1000 miles.
9. Model selection is the task of selecting a statistical model from a set of candidate models
and the economic meaning is one important criterion to choose a model. Given candidate
models of similar predictive or explanatory power, the simplest model is most likely to
be correct.
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